Modeling positive and negative information in possibility theory

• Authors: Salem Benferhat;Didier Dubois;Souhila Kaci;Henri Prade
• Venue: International Journal of Intelligent Systems - Bipolar Representations of Information and Preference Part 2: Reasoning and Learning
• Year: 2008

From a knowledge representation point of view, it may be interesting to distinguish between (i) what is potentially possible because it is not inconsistent with the available knowledge on the one hand, and (ii) what is actually possible because it is reported from observations on the other hand. Such a distinction also makes sense when expressing preferences, to point out positively desired choices among merely tolerated ones. Possibility theory provides a representation framework where this distinction can be made in a graded way. The two types of information can be encoded by two types of constraints expressed in terms of necessity measures and in terms of so-called guaranteed possibility functions. These two set-functions are min-decomposable with respect to conjunction and disjunction, respectively. This gives birth to two forms of possibilistic logic bases, where clauses (resp., phrases) are weighted in terms of a necessity measure (resp., a guaranteed possibility function). By application of a minimal commitment principle, the two bases induce a pair of possibility distributions at the semantic level, for which a consistency condition should hold to ensure that what is claimed to be actually possible is indeed not impossible. The paper provides a survey of this bipolar representation framework, including the use of conditional measures, or the handling of comparative context-dependent constraints. The interest of the framework is stressed for expressing preferences, as well as in the representation of “if–then” rules in terms of examples and counterexamples. © 2008 Wiley Periodicals, Inc. A preliminary version of this work was presented by the last author at the Machine Intelligence 19 Workshop, held at Withersdane Conference Centre, Imperial College at Wye on September 18–20, 2002 (still accessible at ). A revised version should have appeared in the Electronic Transactions on Artificial Intelligence (ETAI; ) among selected articles from the Machine Intelligence 19 Workshop. It has been announced for many years as Volume 6 of ETAI, but never made accessible since then. The present version is a fully revised (again) and updated version of the previous one.